Paper 2023/1620

Commitments from Quantum One-Wayness

Dakshita Khurana, University of Illinois Urbana-Champaign
Kabir Tomer, University of Illinois Urbana-Champaign

One-way functions are central to classical cryptography. They are both necessary for the existence of non-trivial classical cryptosystems, and sufficient to realize meaningful primitives including commitments, pseudorandom generators and digital signatures. At the same time, a mounting body of evidence suggests that assumptions even weaker than one-way functions may suffice for many cryptographic tasks of interest in a quantum world, including bit commitments and secure multi-party computation. This work studies one-way state generators [Morimae-Yamakawa, CRYPTO 2022], a natural quantum relaxation of one-way functions. Given a secret key, a one-way state generator outputs a hard to invert quantum state. A fundamental question is whether this type of quantum one-wayness suffices to realize quantum cryptography. We obtain an affirmative answer to this question by proving that one-way state generators with pure state outputs imply quantum bit commitments and secure multiparty computation. Along the way, we build an intermediate primitive with classical outputs, which we call a (quantum) one-way puzzle. Our main technical contribution is a proof that one-way puzzles imply quantum bit commitments.

Note: Minor updates to the proof of Claim 4.2

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quantumcommitmentone-way statespseudorandom
Contact author(s)
dakshita @ illinois edu
ktomer2 @ illinois edu
2024-01-29: last of 2 revisions
2023-10-19: received
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      author = {Dakshita Khurana and Kabir Tomer},
      title = {Commitments from Quantum One-Wayness},
      howpublished = {Cryptology ePrint Archive, Paper 2023/1620},
      year = {2023},
      note = {\url{}},
      url = {}
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